Born in Nishapur, at a young age he moved toSamarkand and obtained his education there. Afterwards he moved to Bukhara and became established as one of the major mathematicians and astronomers of the medieval period. He is the author of one of the most important treatises on algebra written before modern times, the Treatise on Demonstration of Problems of Algebra, which includes a geometric method for solving cubic equations by intersecting a hyperbola with acircle.[4] He contributed to a calendar reform.

His significance as a philosopher and teacher, and his few remaining philosophical works, have not received the same attention as his scientific and poetic writings. Al-Zamakhshari referred to him as “the philosopher of the world”. Many sources have testified that he taught for decades the philosophy of Avicenna in Nishapur where Khayyám was born and buried and where his mausoleum today remains a masterpiece of Iranian architecturevisited by many people every year.[5]

Outside Iran and Persian speaking countries, Khayyám has had an impact on literature and societies through the translation of his works and popularization by other scholars. The greatest such impact was in English-speaking countries; the English scholar Thomas Hyde(1636–1703) was the first non-Persian to study him. The most influential of all was Edward FitzGerald (1809–83),[6] who made Khayyám the most famous poet of the East in the West through his celebrated translation and adaptations of Khayyám's rather small number of quatrains (Persian: رباعیات‎ rubāʿiyāt) in the Rubaiyat of Omar Khayyam.

Name explanation

غیاث ‌الدین Ghiyāth ad-Din - means "the Shoulder of the Faith" and implies the knowledge of the Quran.ابوالفتح عمر بن ابراهیم Abu'l-Fat'h 'Umar ibn Ibrāhīm - Abu means father, Fat'h means conqueror, 'Umar means life, Ibrahim is the name of the father.خیام Khayyām - means "tent maker" it is a byname derived from the father's craft.نیشابورﻯ Nīshāpūrī - is the link to his hometown of Nishapur.

Ghiyāth ad-Din Abu'l-Fat'h 'Umar ibn Ibrāhīm al-Khayyām Nīshāpūrī (Persian: غیاث الدین ابو الفتح عمر ابراهیم خیام نیشاپوری‎) was born in Nishapur, modern-day Iran, but then a Seljuq capital in Khorasan,[7][8][9] which rivaled Cairo or Baghdad in cultural prominence in that era. He is thought to have been born into a family of tent-makers (khayyāmī "tent-maker"), which he would make into a play on words later in life:

He spent part of his childhood in the town of Balkh (in present-day northern Afghanistan), studying under the well-known scholar Sheikh Muhammad Mansuri. He later studied under Imam Mowaffaq Nishapuri, who was considered one of the greatest teachers of the Khorasan region. Throughout his life Omar Khayyám was tireless in his efforts; by day he would teach algebra and geometry, in the evening he would attend the Seljuq court as an adviser of Malik-Shah I,[10] and at night he would studyastronomy and complete important aspects of the Jalali calendar.

Omar Khayyám's years in Isfahan were very productive ones, but after the death of the Seljuq SultanMalik-Shah I (presumably by the Assassins sect), the Sultan's widow turned against him as an adviser, and as a result, he soon set out on his Hajj or pilgrimage to Mecca and Medina. He was then allowed to work as a court astrologer, and was permitted to return to Nishapur, where he was renowned for his works, and continued to teach mathematics, astronomy and even medicine.[1]

Khayyám Sikander was famous during his times as a mathematician. He wrote the influential Treatise on Demonstration of Problems of Algebra (1070), which laid down the principles of algebra, part of the body of Persian Mathematics that was eventually transmitted to Europe. In particular, he derived general methods for solving cubic equations and even some higher orders.Khayyám himself rejects to be associated with the titlefalsafī"philosopher" in the sense of Aristotelianism and stressed he wishes "to know who I am". In the context of philosophers he was labeled by some of his contemporaries as "detached from divine blessings".[43]

It is now established that Khayyám taught for decades the philosophy of Avicena, especially the Book of Healing, in his home town Nishapur, till his death.[5] In an incident he had been requested to comment on a disagreement between Avicena and a philosopher called Abu'l-Barakāt al-Baghdādī who had criticizedAvicena strongly. Khayyám is said to have answered "[he] does not even understand the sense of the words of Avicenna, how can he oppose what he does not know?"[43]

Mathematical order: From where does this order issue, and why does it correspond to the world of nature? His answer is in one of his philosophical "treatises on being". Khayyám's answer is that "the Divine Origin of all existence not only emanates wujud "being", by virtue of which all things gain reality, but It is the source of order that is inseparable from the very act of existence."[44]

The significance of axioms in geometry and the necessity for the mathematician to rely upon philosophy and hence the importance of the relation of any particular science to prime philosophy. This is the philosophical background to Khayyám's total rejection of any attempt to "prove" the parallel postulate, and in turn his refusal to bring motion into the attempt to prove this postulate, as had Ibn al-Haytham, because Khayyám associated motion with the world of matter, and wanted to keep it away from the purely intelligible and immaterial world of geometry.[44]

Clear distinction made by Khayyám, on the basis of the work of earlier Persian philosophers such as Avicenna, between natural bodies and mathematical bodies. The first is defined as a body that is in the category of substance and that stands by itself, and hence a subject ofnatural sciences, while the second, called "volume", is of the category of accidents (attributes) that do not subsist by themselves in the external world and hence is the concern of mathematics. Khayyám was very careful to respect the boundaries of each discipline, and criticized ibn al-Haytham in his proof of the parallel postulate precisely because he had broken this rule and had brought a subject belonging to natural philosophy, that is, motion, which belongs to natural bodies, into the domain of geometry, which deals with mathematical bodies.[44]

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“And what reason have you that you should not fight in the way of Allah and of the weak among the men and the women and the children, (of) those who say: Our Lord! Cause us to go forth from this town, whose people are oppressors, and give us from Thee a guardian and give us from Thee a helper.”